Neper

The neper (symbol: Np) is a logarithmic unit for ratios of measurements of physical field and power quantities, such as gain and loss of electronic signals. The unit's name is derived from the name of John Napier, the inventor of logarithms. As is the case for the decibel and bel, the neper is a unit defined in the international standard ISO 80000. It is not part of the International System of Units (SI), but is accepted for use alongside the SI.[1]

Definition

Like the decibel, the neper is a unit in a logarithmic scale. While the bel uses the decadic (base-10) logarithm to compute ratios, the neper uses the natural logarithm, based on Euler's number (e ≈ 2.71828). The value of a ratio in nepers is given by

where and are the values of interest (amplitudes), and ln is the natural logarithm. When the values are quadratic in the amplitude (e.g. power), they are first linearised by taking the square root before the logarithm is taken, or equivalently the result is halved.

In the International System of Quantities, the neper is defined as 1 Np = 1.[2]

Units

The neper is defined in terms of ratios of field quantities — also called root-power quantities — (for example, voltage or current amplitudes in electrical circuits, or pressure in acoustics), whereas the decibel was originally defined in terms of power ratios. A power ratio 10 log r dB is equivalent to a field-quantity ratio 20 log r dB, since power in a linear system is proportional to the square (Joule's laws) of the amplitude. Hence the decibel and the neper have a fixed ratio to each other:

and

The (voltage) level ratio is

Like the decibel, the neper is a dimensionless unit. The International Telecommunication Union (ITU) recognizes both units. Only the neper is coherent with the SI.[3]

Applications

The neper is a natural linear unit of relative difference, meaning in nepers (logarithmic units) relative differences add rather than multiply. This property is shared with logarithmic units in other bases, such as the bel.

Particular to the neper, however, is that the derived unit of centineper is asymptotically equal to percentage difference for very small differences – since the derivative of the natural log (at 1) is 1; this is not shared with other logarithmic units, which introduce a scaling factor due to the derivative not being unity. The centineper can thus be used as a linear replacement for percentage differences. The linear approximation for small percentage differences,

is widely used, particularly in finance—see for example the Fisher equation. However, it is only approximate, with error increasing for large percentage changes. Measured instead in centinepers, these linear approximations can be replaced with exact equalities, and applicable to any magnitude change, by defining the following centineper quantity for any change

See also

Notes and references

  1. ^ Bureau International des Poids et Mesures (2006), The International System of Units (SI) Brochure, 8th edition, pp. 127–128.
  2. ^ Thor, A. J. (1994). New International Standards for Quantities and Units. Metrologia, 30(5), 517.
  3. ^ ISO 80000-3:2007 §0.5

Further reading

  • Tuffentsammer, Karl (1956). "Das Dezilog, eine Brücke zwischen Logarithmen, Dezibel, Neper und Normzahlen" [The decilog, a bridge between logarithms, decibel, neper and preferred numbers]. VDI-Zeitschrift (in German). 98: 267–274.
  • Paulin, Eugen (2007-09-01). Logarithmen, Normzahlen, Dezibel, Neper, Phon - natürlich verwandt! [Logarithms, preferred numbers, decibel, neper, phon - naturally related!] (PDF) (in German). Archived (PDF) from the original on 2016-12-18. Retrieved 2016-12-18.

External links

Banachiewicz (crater)

Banachiewicz is a largely degraded lunar impact crater that is located near the eastern limb of the Moon. It was named after Polish astronomer Tadeusz Banachiewicz. Due to its location, this crater appears very foreshortened, the visibility is also more than partly affected by libration, which can completely conceal this formation from view.

Portions of the western and southwest rim still survive as low ridges in the surface, while the remainder is a jumble of irregular terrain with little definition. There are two small impact craters of note within the interior: Banachiewicz B is adjacent to the western rim, while the smaller Knox-Shaw is located closer to the midpoint.

Just to the northeast of this formation is the large walled plain Neper, which lies on the southern edge of Mare Marginis. The crater Schubert is located to the south of Banachiewicz, while Schubert E is attached to the exterior of the western rim.

Field, power, and root-power quantities

A power quantity is a power or a quantity directly proportional to power, e.g., energy density, acoustic intensity, and luminous intensity. Energy quantities may also be labelled as power quantities in this context.A root-power quantity is a quantity such as voltage, current, sound pressure, electric field strength, speed, or charge density, the square of which, in linear systems, is proportional to power. The term root-power quantity was introduced in the ISO 80000-1 § Annex C; it replaces and deprecates the term field quantity.

It is essential to know which category a measurement belongs to when using decibels (dB) for comparing the levels of such quantities. A change of one bel in the level corresponds to a 10× change in power, so when comparing power quantities x and y, the difference is defined to be 10×log10(y/x) decibel. With root-power quantities, however the difference is defined as 20×log10(y/x) dB. In linear systems, these definitions allow the distinction between root-power quantities and power quantities to be ignored when specifying changes as levels: an amplifier can be described as having "3 dB" of gain without needing to specify whether voltage or power are being compared; for a given linear load (e.g. an 8 Ω speaker), such an increase will result in a 3 dB increase in both the sound pressure level and the sound power level at a given location near the speaker. Conversely, when ratios cannot be identified as either power or root-power quantities, the units neper (Np) and decibel (dB) cannot be sensibly used.

In the analysis of signals and systems using sinusoids, field quantities and root-power quantities may be complex-valued.

Goddard (crater)

Goddard is a lunar impact crater that is located along the eastern limb of the Moon, and so is visible from the edge from Earth. It is best viewed during favorable librations when the orientation of the Moon brings it further into sight. The crater is located in the Mare Marginis, to the northeast of the prominent crater Neper. Ibn Yunus, a crater remnant, is attached to the southeastern rim, and is partly overlaid by Goddard. To the northeast is Al-Biruni.

The rim of Goddard has nearly been destroyed along the southern edge, and the interior floor is connected to the surrounding mare through gaps in this section of the wall. The remainder of the rim is significantly eroded and worn, leaving only a ring of rugged ground surrounding the inner floor.

The floor of the crater has been resurfaced in the past by lava floods, leaving the interior nearly flat and featureless. There is no central peak, and only a few tiny craterlets mark the surface. The most prominent of these is a matched pair of small craterlets in the south-southwest part of the floor.

This feature is named after the pioneering rocket scientist Robert H. Goddard.

Hapi (Nile god)

Hapi was the god of the annual flooding of the Nile in ancient Egyptian religion. The flood deposited rich silt (fertile soil) on the river's banks, allowing the Egyptians to grow crops. Hapi was greatly celebrated among the Egyptians. Some of the titles of Hapi were "Lord of the Fish and Birds of the Marshes" and "Lord of the River Bringing Vegetation". Hapi is typically depicted as an androgynous figure with a large belly and pendulous breasts, wearing a loincloth and ceremonial false beard.

Hemsut

In Egyptian mythology, Hemsut (or Hemuset) was the goddess of fate and protection. She is representative of the ka. Her headdress bears a shield, above which are two crossed arrows.

John Napier

John Napier of Merchiston (; 1550 – 4 April 1617); also signed as Neper, Nepair; nicknamed Marvellous Merchiston) was a Scottish landowner known as a mathematician, physicist, and astronomer. He was the 8th Laird of Merchiston. His Latinized name was Ioannes Neper.

John Napier is best known as the discoverer of logarithms. He also invented the so-called "Napier's bones" and made common the use of the decimal point in arithmetic and mathematics.

Napier's birthplace, Merchiston Tower in Edinburgh, is now part of the facilities of Edinburgh Napier University. Napier died from the effects of gout at home at Merchiston Castle and his remains were buried in the kirkyard of St Giles. Following the loss of the kirkyard there to build Parliament House, he was memorialised at St Cuthbert's at the west side of Edinburgh.

Level (logarithmic quantity)

In science and engineering, a power level and a field level (also called a root-power level) are logarithmic measures of certain quantities referenced to a standard reference value of the same type.

A power level is a logarithmic quantity used to measure power, power density or sometimes energy, with commonly used unit decibel (dB).

A field level (or root-power level) is a logarithmic quantity used to measure quantities of which the square is typically proportional to power, etc., with commonly used units neper (Np) or decibel (dB).The type of level and choice of units indicate the scaling of the logarithm of the ratio between the quantity and it reference value, though a logarithm may be considered to be a dimensionless quantity. The reference values for each type of quantity are often specified by international standards.

Power and field levels are used in electronic engineering, telecommunications, acoustics and related disciplines. Power levels are used for signal power, noise power, sound power, sound exposure, etc. Field levels are used for voltage, current, sound pressure.

Logarithmic scale

A logarithmic scale is a nonlinear scale used for a large range of positive multiples of some quantity. Common uses include earthquake strength, sound loudness, light intensity, and pH of solutions.

It is based on orders of magnitude, rather than a standard linear scale, so the value represented by each equidistant mark on the scale is the value at the previous mark multiplied by a constant.

Logarithmic scales are also used in slide rules for multiplying or dividing numbers by adding or subtracting lengths on the scales.

Mare Smythii

Mare Smythii (Latin for "Sea of Smyth") is a lunar mare located along the equator on the easternmost edge of the lunar near side. The Smythii basin where the mare is located is of the Pre-Nectarian epoch, while the surrounding features are of the Nectarian system. The mare material, which make up the floor of the mare, is a high aluminous basalt, and consists of Upper Imbrian basalt covered by Eratosthenian basalt.

Mare Smythii contains a relatively high number of craters with fractured floors, including the noticeably unusual crater Haldane. This is probably a result of uplift from injection of magma below the mare.The crater Neper is located to the north of the mare. This crater makes up part of the southern rim of Mare Marginis. Just off to the northwest of the mare are the craters Schubert and Schubert B. The dark mare-filled crater at the southern edge of Smythii is the crater Kästner.

The Mare Smythii is named for the 19th century British astronomer William Henry Smyth.

National Center of Cinematography (Albania)

The Albania National Center of Cinematography (Albanian: Kinostudio Shqipëria e Re) is the largest film distributor and film production company in the cinema of Albania connected with over 700 films (feature films and documentaries) between 1947 and 2012. The studio has produced and distributed the vast majority of Albanian films. Especially important was its work in the 1970s and 1980s when the studio averaged 75–80 movies per year.

Neper (crater)

Neper is an old lunar impact crater located near the eastern limb of the Moon. Due to its location the crater must be viewed during a suitable libration, and is very foreshortened. The crater lies on the south edge of Mare Marginis, to the east of the crater Jansky. To the northwest across the Mare Marginis is the crater Goddard.

The crater inner walls have worn terraces, with low rim edges at the northern and southern extremes. The crater floor is dark and flat, with a central peak and several crater impacts near the west rim. The most notable of these is a small crater near the north-northwestern edge.

It is named after the Scottish mathematician, physicist, astronomer and astrologer John Napier.

Neper (disambiguation)

Neper is a logarithmic unit of ratio.

Neper may also refer to:

John Napier, a Scottish mathematician

Neper (crater), a lunar impact crater

Neper (mythology), an Egyptian deity

Neper (mythology)

In ancient Egyptian religion, Neper (alts. Nepra or Nepri) was a god of grain. His female counterpart was Nepit, the goddess of grain. His consort may have been Tayt, the goddess of weaving.

Sabatier (crater)

Sabatier is a small lunar impact crater that is located near the eastern limb of the Moon, at the southwestern fringes of the Mare Marginis.

It lies in a relatively isolated area, with the nearest named crater being the walled plain Neper to the southeast. This is a nearly circular formation, with a low outer rim and a circular floor about half the crater's diameter.

Schubert (lunar crater)

Schubert is a lunar impact crater that lies near the eastern limb of the Moon's near side. The crater is located to the northwest of the Mare Smythii, and southwest of the prominent crater Neper. Nearly attached to the southern rim is the crater Back.

Schubert is a nearly circular crater formation that has not suffered significant erosion from subsequent impacts, and retains a well-defined rim. The interior surface is generally flat, a few low hills near the center.

Sound exposure

Sound exposure is the integral, over time, of squared sound pressure. The SI unit of sound exposure is the pascal squared second (Pa2·s).

Tacchini (crater)

Tacchini is a lunar impact crater on the northwestern edge of the Mare Smythii, near the eastern limb of the Moon. It was named after Italian astronomer Pietro Tacchini. It lies just to the south of the prominent crater Neper, and was designated Neper K before being given its current name by the IAU. To the west-southwest of Tacchini is the crater pair of Schubert and Back.

This crater is roughly circular in form, with a rim that is better defined along the eastern side. The northwestern half of the floor is elevated, along the side where ejecta from the younger Neper intrudes into the interior. There is a pair of small craters along the northwestern inner wall.

Tayt

Tayt (also Tait, Tayet, and Taytet) was an Egyptian goddess. Some attest her husband was Neper while others state she was possibly the consort of Hedjhotep.

Virchow (crater)

Virchow is a small lunar impact crater that is located on the northwestern interior floor of the prominent crater Neper. The latter formation lies near the eastern limb of the Moon, along the southern edge of the Mare Marginis. Observation of this area is hindered due to foreshortening, as well as libration effects. It was named after German physician Rudolf Virchow in 1979. Before, this crater had the designation Neper G.

Virchow has a distorted shape, with a somewhat polygonal rim, particularly in the northern half. The northwestern rim protrudes outwards, giving the crater an asymmetrical appearance. This section of the rim just makes contact with the inner wall of Neper crater. The inner walls of Virchow are relatively narrow, and the interior floor is nearly level and almost featureless.

Base units
Derived units
with special names
Other accepted units
See also

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